editText is a part of alertDialog layout so Just access editText with reference of alertDialog

EditText editText = (EditText) alertDialog.findViewById(R.id.label_field);

Update:

Because in code line dialogBuilder.setView(inflater.inflate(R.layout.alert_label_editor, null));

inflater is Null.

update your code like below, and try to understand the each code line

AlertDialog.Builder dialogBuilder = new AlertDialog.Builder(this);
// ...Irrelevant code for customizing the buttons and title
LayoutInflater inflater = this.getLayoutInflater();
View dialogView = inflater.inflate(R.layout.alert_label_editor, null);
dialogBuilder.setView(dialogView);

EditText editText = (EditText) dialogView.findViewById(R.id.label_field);
editText.setText("test label");
AlertDialog alertDialog = dialogBuilder.create();
alertDialog.show();

Update 2:

As you are using View object created by Inflater to update UI components else you can directly use setView(int layourResId) method of AlertDialog.Builder class, which is available from API 21 and onwards.